MathDB

Not hard but cute (points lying on a circle)

Source: IMO Shortlist 2005; Polish second round 2006; Costa Rica final round 2006

February 24, 2006

geometrycircumcirclehomothetyIMO Shortlisttriangle -incenter

Problem Statement

Given a triangle

ABC

satisfying

AC+BC=3\cdot AB

. The incircle of triangle

ABC

has center

I

and touches the sides

BC

and

CA

at the points

D

and

E

, respectively. Let

K

and

L

be the reflections of the points

D

and

E

with respect to

I

. Prove that the points

A

B

K

L

lie on one circle.
Proposed by Dimitris Kontogiannis, Greece